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arXiv · 1411.2747

Inequalities and bilipschitz conditions for triangular ratio metric

Parisa Hariri·Matti Vuorinen·Xiaohui Zhang
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Abstract

Let $G \subsetneq \mathbb{R}^n$ be a domain and let $d_1$ and $d_2$ be two metrics on $G$. We compare the geometries defined by the two metrics to each other for several pairs of metrics. The metrics we study include the distance ratio metric, the triangular ratio metric and the visual angle metric. Finally we apply our results to study Lipschitz maps with respect to these metrics.

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Parisa Hariri, Matti Vuorinen, Xiaohui Zhang. 2014-11-11. Inequalities and bilipschitz conditions for triangular ratio metric. https://doi.org/10.1216/rmj-2017-47-4-1121

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